**Mars landing.**We will be investigating the latest Mars rover mission ("Curiosity") this week starting today. We'll watch the "7 minutes of Terror" and hand out the Curiosity questions. You have the rest of this week to review the Curiosity questions and come up with a rationale for your answers. You may compile notes that you can refer to on Friday but the work you turn in must be performed start to finish in Friday's class.

**If you missed school today:**

- Watch the "7 minutes of Terror" video.
- Download and complete the Physics worksheets (problems 1 and 2).
- Begin working on the Curiosity Mars mission homework problems below. Try to answer at least the first problem on your own.
- Read "10 ideas the world needs" (printable copies: word format or pdf ).

**Rocket Propulsion**

The main task for Friday is to answer the following list of questions related to Curiosity. Each question has a certain number of "experience" points that can be earned. The harder the question, the more points possible. Your grade for the assignment will be determined by how many experience points you can accumulate during the 2 hour block. You should know that the more detailed your answer (that is, answers that demonstrate thoughtful consideration and an appreciation of the physics involved), the more points you can earn. Answers that can be easily copied (single numbers without work) will receive at most half credit. Answers that show you have put out considerable effort and are at least reasonable can receive full credit even if incorrect. Notice that there are a number of web resources listed at the end of the problems below and that there are helpful hints at the bottom of this page.

**Mars Curiosity Rover Homework**

Assignment By Rhett Allain

Mars Science Laboratory landed its rover, Curiosity, on Mars on August 5 (10:31 PM PDT) 2012. What better way to celebrate this mission than with homework questions. Note: some of these are rather advanced level and may require looking up some information as well as perhaps some numerical calculations or something.

I based these questions on the mission animation video. You can assume that everything in the video is accurate enough to be real – in case you want to answer any questions with a video analysis. One more note. I am just coming up with questions as I think of them. There is no solutions manual and some of the questions might not even be valid to ask. For invalid questions, just explain why it is not valid.

**1. Solar Panels**

How much does the average solar light intensity change as the spacecraft goes to Mars? Estimate the power the spacecraft will get from its solar panels.

**2. Average Speed**

- If the spacecraft takes 8.5 months to make it to Mars, what was the average speed? Estimate until the cows come home. You don’t need an exact value – just a ball park figure. What things did you assume in your calculation?
- If the spacecraft went in a straight line directly away from the Sun, how much would it slow down during its journey? This one is tricky. Be sure to refer to the hint below.

**3. Change in Energy**

What is the change in energy for the spacecraft (with heat shield) as it goes through re-entry? Assume it slows down to terminal speed of 450 meters.sec and starts with the average speed that you calculated in question 2. You can use the site http://www.spaceflight101.com/msl-landing-special.html for this information.

**4. Heat Capacity**

Getting rid of all this energy in a short amount of time is critical or the spacecraft will literally burn up. The heat shield puts about half of this energy into the Mars atmosphere while the other half goes into increasing the thermal energy of the heat shield. We can estimate the physical properties of the heat shield by using a familiar equation from calorimetry. Calorimetry studies how heat is absorbed and exchanged between systems. The temperature change in a substance for a given amount of energy input is given by the equation E=mcTwhere E is the energy in Joules, m is the mass in grams, c is the substance’s heat capacity, and T is the temperature change in degrees Celsius. Each substance has a difference capacity to absorb heat energy given by c. Heat shields must be light but able to absorb vast amounts of heat. If you estimate the heat shield to have a mass of 100 kg, what would the heat capacity of the heat shield be? You can assume the initial temperature of the heat shield in space is -100 degrees Celsius. Don’t forget that only half of the energy is absorbed by the heat shield.

**5. Thrust**

- Suppose the rockets have just enough thrust for the whole spacecraft to hover. What is the value of thrust needed for the surface of Mars?
- When the rover is released from the decent stage, the rockets no longer have to support as much mass. What is the approximate acceleration of the decent stage (the part with the rockets) after the rover is deployed?

**Cheating**

Don’t cheat. Cheaters never win. What would be cheating in this case? Well, if you need to look up values for the dimensions, mass or material of some object that is OK. If you need to look up planetary data (like mass and radius of Mars) – again, OK. If you want to answer the thrust question by looking it up on NASA’s site, that would be bad (cheating). But if you look up the mass of the spacecraft on the same site, that would be ok. Oh, Wikipedia’s page on Curiosity is pretty useful too.

Rhett Allain is an Associate Professor of Physics at Southeastern Louisiana University. He enjoys teaching and talking about physics. Sometimes he takes things apart and can't put them back together.

**Helpful links to answer these questions:**

MSL Landing Special - Be sure to watch the "7 minutes of terror" if you missed it in class

How to calculate terminal velocity - how fast something can fall

How to calculate escape velocity - how fast something needs to be traveling to escape gravity

How far away is Mars - some data to help you estimate the distance the MSL travelled

Gravitational energy - equations to calculate changes in gravitational energy

MSL specs - useful source of masses, dimensions, etc on the Mars Science Laboratory mission

Converting potential energy into kinetic energy - useful for problem 2

Why the travel path of the spacecraft isn't a straight line :http://www.qrg.northwestern.edu/projects/vss/docs/space-environment/zoom-travel.html

How to calculate the gravitational force between two objects (note that this describes FORCE, not ENERGY. There is a difference): http://www.school-for-champions.com/science/gravitation_force_objects.htm

Mass and radii of planets: http://library.thinkquest.org/TQ0312074/evtable.htm

**HINTS:**

**Problem 1:**Light expands SPHERICALLY from a point source. Intensity is therefore inversely proportional to the surface area of a sphere with a radius equal to the distance from the source. Intensity will decrease at the same rate that the sphere's surface area increases. You will have to make a number of assumptions about the solar cells. Just be sure you state what assumptions you use.

**Problem 2:**Be sure to mention what distance you use as the distance between earth and mars. There are many possibilities. The second question is tricky. Imagine a ball rolling up a hill. As the ball goes up, its kinetic energy is converted into potential energy. Similarly, as the spacecraft moves away from the sun, it is climbing up a gravitational hill. It will also have to "spend" part of its kinetic energy to move "up" the hill to mars. If you know the gravitational energy of the spacecraft at earth and at mars, the difference is the "height" of the gravitational hill. Equating this to the expression for kinetic energy allows you to see how much velocity it will take to get there (without falling back).

**Problem 3:**Since the only energy that is changing at re-entry is the kinetic energy, all you need are the starting and ending speeds, the mass of the spacecraft (make sure it has all the right pieces), and the equation for kinetic energy (our old friend, 1/2 mv**2).

**Problem 4:**There's only one number not provided in this problem (the highest temperature). That was in the video as well in a number of other locations.

**Problem 5:**This final problem involves forces, not energies. When two opposing forces balance, they must be equal. Thus, when hovering, the weight of the spacecraft (its mass times the martian gravity or "mg") must equal the force ("thrust") of the rocket. If you know "m" and "g", you know the balancing thrust. Remember that the acceleration due to gravity on mars is very different that on earth (it's most certainly NOT 9.8!). Once you know the thrust for the whole craft, what will happen when the Curiosity part of the mass is cut loose? The thrust doesn't change, but the total mass did. The net force acting on the descent vehicle is no longer zero. First calculate the new net force (this will require a subtraction). Then, set that equal to "ma" and solve for the new acceleration ("a").

Begin reading the "10 ideas the world needs" (printable copies: word format or pdf ).